Before Calculus | p. 1 |

Functions | p. 1 |

New Functions from Old | p. 15 |

Families of Functions | p. 27 |

Inverse Functions | p. 38 |

Limits And Continuity | p. 49 |

Limits (An Intuitive Approach) | p. 49 |

Computing Limits | p. 62 |

Limits at Infinity; End Behavior of a Function | p. 71 |

Limits (Discussed More Rigorously) | p. 81 |

Continuity | p. 90 |

Continuity of Trigonometric Functions | p. 101 |

The Derivative | p. 110 |

Tangent Lines and Rates of Change | p. 110 |

The Derivative Function | p. 122 |

Introduction to Techniques of Differentiation | p. 134 |

The Product and Quotient Rules | p. 142 |

Derivatives of Trigonometric Functions | p. 148 |

The Chain Rule | p. 153 |

Implicit Differentiation | p. 161 |

Related Rates | p. 168 |

Local Linear Approximation; Differentials | p. 175 |

The Derivative In Graphing And Applications | p. 187 |

Analysis of Functions I: Increase, Decrease, and Concavity | p. 187 |

Analysis of Functions II: Relative Extrema; Graphing Polynomials | p. 197 |

Analysis of Functions III: Rational Functions, Cusps, and Vertical Tangents | p. 207 |

Absolute Maxima and Minima | p. 216 |

Applied Maximum and Minimum Problems | p. 224 |

Rectilinear Motion | p. 238 |

Newton's Method | p. 246 |

Rolle's Theorem; Mean-Value Theorem | p. 252 |

Integration | p. 265 |

An Overview of the Area Problem | p. 265 |

The Indefinite Integral | p. 271 |

Integration by Substitution | p. 281 |

The Definition of Area as a Limit; Sigma Notation | p. 287 |

The Definite Integral | p. 300 |

The Fundamental Theorem of Calculus | p. 309 |

Rectilinear Motion Revisited Using Integration | p. 322 |

Average Value of a Function and its Applications | p. 332 |

Evaluating Definite Integrals by Substitution | p. 337 |

Applications Of The Definite Integral In Geometry, Science, And Engineering | p. 347 |

Area Between Two Curves | p. 347 |

Volumes by Slicing; Disks and Washers | p. 355 |

Volumes by Cylindrical Shells | p. 365 |

Length of a Plane Curve | p. 371 |

Area of a Surface of Revolution | p. 377 |

Work | p. 382 |

Moments, Centers of Gravity, and Centroids | p. 391 |

Fluid Pressure and Force | p. 400 |

Exponential, Logarithmic, And Inverse Trigonometric Functions | p. 409 |

Exponential and Logarithmic Functions | p. 409 |

Derivatives and Integrals Involving Logarithmic Functions | p. 420 |

Derivatives of Inverse Functions; Derivatives and Integrals Involving Exponential Functions | p. 427 |

Graphs and Applications Involving Logarithmic and Exponential Functions | p. 434 |

L'Hôpital's Rule; Indeterminate Forms | p. 441 |

Logarithmic and Other Functions Defined by Integrals | p. 450 |

Derivatives and Integrals Involving Inverse Trigonometric Functions | p. 462 |

Hyperbolic Functions and Hanging Cables | p. 472 |

Principles Of Integral Evaluation | p. 488 |

An Overview of Integration Methods | p. 488 |

Integration by Parts | p. 491 |

Integrating Trigonometric Functions | p. 500 |

Trigonometric Substitutions | p. 508 |

Integrating Rational Functions by Partial Fractions | p. 514 |

Using Computer Algebra Systems and Tables of Integrals | p. 523 |

Numerical Integration; Simpson's Rule | p. 533 |

Improper Integrals | p. 547 |

Mathematical Modeling With Differential Equations | p. 561 |

Modeling with Differential Equations | p. 561 |

Separation of Variables | p. 568 |

Slope Fields; Euler's Method | p. 579 |

First-Order Differential Equations and Applications | p. 586 |

Infinite Series | p. 596 |

Sequences | p. 596 |

Monotone Sequences | p. 607 |

Infinite Series | p. 614 |

Convergence Tests | p. 623 |

The Comparison, Ratio, and Root Tests | p. 631 |

Alternating Series; Absolute and Conditional Convergence | p. 638 |

Maclaurin and Taylor Polynomials | p. 648 |

Maclaurin and Taylor Series; Power Series | p. 659 |

Convergence of Taylor Series | p. 668 |

Differentiating and Integrating Power Series; Modeling with Taylor Series | p. 678 |

Parametric And Polar Curves; Conic Sections | p. 692 |

Parametric Equations; Tangent Lines and Arc Length for Parametric Curves | p. 692 |

Polar Coordinates | p. 705 |

Tangent Lines, Arc Length, and Area for Polar Curves | p. 719 |

Conic Sections | p. 730 |

Rotation of Axes; Second-Degree Equations | p. 748 |

Conic Sections in Polar Coordinates 754 A APPENDICES A GRAPHING FUNCTIONS USING CALCULATORS AND COMPUTER ALGEBRA SYSTEMS A1 B TRIGONOMETRY REVIEW A13 C SOLVING POLYNOMIAL EQUATIONS A27 D SELECTED PROOFS A34 ANSWERS TO ODD-NUMBERED EXERCISES A45 | |

Index | p. I-1 |

Web Appendices (online only) | |

Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS | |

Real Numbers, Intervals, And Inequalities | |

Absolute Value | |

Coordinate Planes, Lines, And Linear Functions | |

Distance, Circles, And Quadratic Equations | |

Early Parametric Equations Option | |

Mathematical Models | |

The Discriminant | |

Second-Order Linear Homogeneous Differential Equations | |

Web Projects: Expanding the Calculus Horizon (online only) | |

Available for download atwww.wiley.com/college/anton or atwww.howardanton.com and in WileyPLUS | |

Blammo The Human Cannonball | |

Comet Collision | |

Hurricane Modeling | |

Iteration And Dynamical Systems | |

Railroad Design | |

Robotics | |

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